





class 							__SCREAMING_SNAKE_CASE       :






							def __init__(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	,			__lowerCAmelCase	):
														UpperCamelCase__					  =      None
														UpperCamelCase__					  =      None
														UpperCamelCase__					  =      graph

														self._normalize_graph(__lowerCAmelCase	,			__lowerCAmelCase	)
														UpperCamelCase__					  =      len(__lowerCAmelCase	)
														UpperCamelCase__					  =      None






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	):
														if sources is int:
																					UpperCamelCase__					  =      [sources]
														if sinks is int:
																					UpperCamelCase__					  =      [sinks]

														if len(__lowerCAmelCase	) == 0 or len(__lowerCAmelCase	) == 0:
																					return

														UpperCamelCase__					  =      sources[0]
														UpperCamelCase__					  =      sinks[0]

														# make fake vertex if there are more
														# than one source or sink
														if len(__lowerCAmelCase	) > 1 or len(__lowerCAmelCase	) > 1:
																					UpperCamelCase__					  =      0
																					for i in sources:
																												max_input_flow += sum(self.graph[i]	)

																					UpperCamelCase__					  =      len(self.graph	) + 1
																					for room in self.graph:
																												room.insert(0	,			0	)
																					self.graph.insert(0	,			[0] * size	)
																					for i in sources:
																												UpperCamelCase__					  =      max_input_flow
																					UpperCamelCase__					  =      0

																					UpperCamelCase__					  =      len(self.graph	) + 1
																					for room in self.graph:
																												room.append(0	)
																					self.graph.append([0] * size	)
																					for i in sinks:
																												UpperCamelCase__					  =      max_input_flow
																					UpperCamelCase__					  =      size - 1






							def 					_lowerCamelCase		(    self	):
														if self.maximum_flow_algorithm is None:
																					raise Exception("""You need to set maximum flow algorithm before."""	)
														if self.source_index is None or self.sink_index is None:
																					return 0

														self.maximum_flow_algorithm.execute()
														return self.maximum_flow_algorithm.getMaximumFlow()







							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	):
														UpperCamelCase__					  =      algorithm(self	)






class 							__SCREAMING_SNAKE_CASE       :






							def __init__(    self	,			__lowerCAmelCase	):
														UpperCamelCase__					  =      flow_network
														UpperCamelCase__					  =      flow_network.verticesCount
														UpperCamelCase__					  =      flow_network.sourceIndex
														UpperCamelCase__					  =      flow_network.sinkIndex
														# it's just a reference, so you shouldn't change
														# it in your algorithms, use deep copy before doing that
														UpperCamelCase__					  =      flow_network.graph
														UpperCamelCase__					  =      False






							def 					_lowerCamelCase		(    self	):
														if not self.executed:
																					self._algorithm()
																					UpperCamelCase__					  =      True







							def 					_lowerCamelCase		(    self	):
														pass






class 							__SCREAMING_SNAKE_CASE       (  _UpperCAmelCase							):






							def __init__(    self	,			__lowerCAmelCase	):
														super().__init__(__lowerCAmelCase	)
														# use this to save your result
														UpperCamelCase__					  =      -1







							def 					_lowerCamelCase		(    self	):
														if not self.executed:
																					raise Exception("""You should execute algorithm before using its result!"""	)

														return self.maximum_flow






class 							__SCREAMING_SNAKE_CASE       (  _UpperCAmelCase							):






							def __init__(    self	,			__lowerCAmelCase	):
														super().__init__(__lowerCAmelCase	)

														UpperCamelCase__					  =      [[0] * self.verticies_count for i in range(self.verticies_count	)]

														UpperCamelCase__					  =      [0] * self.verticies_count
														UpperCamelCase__					  =      [0] * self.verticies_count






							def 					_lowerCamelCase		(    self	):
														UpperCamelCase__					  =      self.verticies_count

														# push some substance to graph
														for nextvertex_index, bandwidth in enumerate(self.graph[self.source_index]	):
																					self.preflow[self.source_index][nextvertex_index] += bandwidth
																					self.preflow[nextvertex_index][self.source_index] -= bandwidth
																					self.excesses[nextvertex_index] += bandwidth

														# Relabel-to-front selection rule
														UpperCamelCase__					  =      [
														    i
														    for i in range(self.verticies_count	)
														    if i != self.source_index and i != self.sink_index
														]

														# move through list
														UpperCamelCase__					  =      0
														while i < len(__lowerCAmelCase	):
																					UpperCamelCase__					  =      vertices_list[i]
																					UpperCamelCase__					  =      self.heights[vertex_index]
																					self.process_vertex(__lowerCAmelCase	)
																					if self.heights[vertex_index] > previous_height:
																												# if it was relabeled, swap elements
																												# and start from 0 index
																												vertices_list.insert(0	,			vertices_list.pop(__lowerCAmelCase	)	)
																												UpperCamelCase__					  =      0
																					else:
																												i += 1

														UpperCamelCase__					  =      sum(self.preflow[self.source_index]	)






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	):
														while self.excesses[vertex_index] > 0:
																					for neighbour_index in range(self.verticies_count	):
																												# if it's neighbour and current vertex is higher
																												if (
																												    self.graph[vertex_index][neighbour_index]
																												    - self.preflow[vertex_index][neighbour_index]
																												    > 0
																												    and self.heights[vertex_index] > self.heights[neighbour_index]
																												):
																																			self.push(__lowerCAmelCase	,			__lowerCAmelCase	)

																					self.relabel(__lowerCAmelCase	)






							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	,			__lowerCAmelCase	):
														UpperCamelCase__					  =      min(
														    self.excesses[from_index]	,			self.graph[from_index][to_index] - self.preflow[from_index][to_index]	,			)
														self.preflow[from_index][to_index] += preflow_delta
														self.preflow[to_index][from_index] -= preflow_delta
														self.excesses[from_index] -= preflow_delta
														self.excesses[to_index] += preflow_delta







							def 					_lowerCamelCase		(    self	,			__lowerCAmelCase	):
														UpperCamelCase__					  =      None
														for to_index in range(self.verticies_count	):
																					if (
																					    self.graph[vertex_index][to_index]
																					    - self.preflow[vertex_index][to_index]
																					    > 0
																					) and (min_height is None or self.heights[to_index] < min_height):
																												UpperCamelCase__					  =      self.heights[to_index]

														if min_height is not None:
																					UpperCamelCase__					  =      min_height + 1


if __name__ == "__main__":
					UpperCamelCase__           =			[0]
					UpperCamelCase__           =			[3]
					# graph = [
					#     [0, 0, 4, 6, 0, 0],
					#     [0, 0, 5, 2, 0, 0],
					#     [0, 0, 0, 0, 4, 4],
					#     [0, 0, 0, 0, 6, 6],
					#     [0, 0, 0, 0, 0, 0],
					#     [0, 0, 0, 0, 0, 0],
					# ]
					UpperCamelCase__           =			[[0, 7, 0, 0], [0, 0, 6, 0], [0, 0, 0, 8], [9, 0, 0, 0]]

					# prepare our network
					UpperCamelCase__           =			FlowNetwork(graph, entrances, exits)
					# set algorithm
					flow_network.set_maximum_flow_algorithm(PushRelabelExecutor)
					# and calculate
					UpperCamelCase__           =			flow_network.find_maximum_flow()

					print(f"""maximum flow is {maximum_flow}""")











"""simple docstring"""





from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


SCREAMING_SNAKE_CASE__   =  {
    "configuration_roberta_prelayernorm": [
        "ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP",
        "RobertaPreLayerNormConfig",
        "RobertaPreLayerNormOnnxConfig",
    ],
}

try:
       if not is_torch_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       SCREAMING_SNAKE_CASE__   =  [
           "ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST",
           "RobertaPreLayerNormForCausalLM",
           "RobertaPreLayerNormForMaskedLM",
           "RobertaPreLayerNormForMultipleChoice",
           "RobertaPreLayerNormForQuestionAnswering",
           "RobertaPreLayerNormForSequenceClassification",
           "RobertaPreLayerNormForTokenClassification",
           "RobertaPreLayerNormModel",
           "RobertaPreLayerNormPreTrainedModel",
       ]

try:
       if not is_tf_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       SCREAMING_SNAKE_CASE__   =  [
           "TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST",
           "TFRobertaPreLayerNormForCausalLM",
           "TFRobertaPreLayerNormForMaskedLM",
           "TFRobertaPreLayerNormForMultipleChoice",
           "TFRobertaPreLayerNormForQuestionAnswering",
           "TFRobertaPreLayerNormForSequenceClassification",
           "TFRobertaPreLayerNormForTokenClassification",
           "TFRobertaPreLayerNormMainLayer",
           "TFRobertaPreLayerNormModel",
           "TFRobertaPreLayerNormPreTrainedModel",
       ]

try:
       if not is_flax_available():
              raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
       pass
else:
       SCREAMING_SNAKE_CASE__   =  [
           "FlaxRobertaPreLayerNormForCausalLM",
           "FlaxRobertaPreLayerNormForMaskedLM",
           "FlaxRobertaPreLayerNormForMultipleChoice",
           "FlaxRobertaPreLayerNormForQuestionAnswering",
           "FlaxRobertaPreLayerNormForSequenceClassification",
           "FlaxRobertaPreLayerNormForTokenClassification",
           "FlaxRobertaPreLayerNormModel",
           "FlaxRobertaPreLayerNormPreTrainedModel",
       ]


if TYPE_CHECKING:
       from .configuration_roberta_prelayernorm import (
           ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
           RobertaPreLayerNormConfig,
           RobertaPreLayerNormOnnxConfig,
       )

       try:
              if not is_torch_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_roberta_prelayernorm import (
                  ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
                  RobertaPreLayerNormForCausalLM,
                  RobertaPreLayerNormForMaskedLM,
                  RobertaPreLayerNormForMultipleChoice,
                  RobertaPreLayerNormForQuestionAnswering,
                  RobertaPreLayerNormForSequenceClassification,
                  RobertaPreLayerNormForTokenClassification,
                  RobertaPreLayerNormModel,
                  RobertaPreLayerNormPreTrainedModel,
              )

       try:
              if not is_tf_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_tf_roberta_prelayernorm import (
                  TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
                  TFRobertaPreLayerNormForCausalLM,
                  TFRobertaPreLayerNormForMaskedLM,
                  TFRobertaPreLayerNormForMultipleChoice,
                  TFRobertaPreLayerNormForQuestionAnswering,
                  TFRobertaPreLayerNormForSequenceClassification,
                  TFRobertaPreLayerNormForTokenClassification,
                  TFRobertaPreLayerNormMainLayer,
                  TFRobertaPreLayerNormModel,
                  TFRobertaPreLayerNormPreTrainedModel,
              )

       try:
              if not is_flax_available():
                     raise OptionalDependencyNotAvailable()
       except OptionalDependencyNotAvailable:
              pass
       else:
              from .modeling_flax_roberta_prelayernorm import (
                  FlaxRobertaPreLayerNormForCausalLM,
                  FlaxRobertaPreLayerNormForMaskedLM,
                  FlaxRobertaPreLayerNormForMultipleChoice,
                  FlaxRobertaPreLayerNormForQuestionAnswering,
                  FlaxRobertaPreLayerNormForSequenceClassification,
                  FlaxRobertaPreLayerNormForTokenClassification,
                  FlaxRobertaPreLayerNormModel,
                  FlaxRobertaPreLayerNormPreTrainedModel,
              )

else:
       import sys

       SCREAMING_SNAKE_CASE__   =  _LazyModule(__name__, globals()["__file__"], _import_structure, module_spec=__spec__)






